Chebyshev Polynomials

The applet below depicts Chebyshev polynomials of the first kind Tn(x) = cos(n·arccos(x)), n = 0, ..., 50.


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Chebyshev Polynomials, plenty


What if applet does not run?

The applet displays the sequence of polynomials PMin through PMax, inclusive. When sufficiently many (30 above) of the polynomial graphs are displayed simultanesoiusly, one can see "ghost lines" -- empty spaces left untouched by the graphs. What are they?


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Chebyshev Polynomials, a few


What if applet does not run?

Both Min and Max numbers in the applet can be clicked on off their vertical center line. To increase the number click to the right of its center line, to decrease it click to the left. Dragging the cursor will speed up the process. 50 is the maximum value for both.

When plenty of the polynomials are graphed there appear some ghost images. What are these?


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